Modeling a low-poly crater in Blender
Lazy tutorial ... 


download (export) terrain high-map from here https://tangrams.github.io


Link is set directly to your Barringer crater. Exported image seems like just a screenshot saved in 8-bit, that makes it lately a bit blocky for displacement (16 or 32-bit would be better for smooth result), but since your goal is low-poly, it's more than enough.




subdivide plane few times to make topology more dense, plus add Subdivide modifier to get grid even more dense to catch details





add Displacement modifier, assign downloaded high-map (greyscale image) as Texture, Strenght = 0.1





add Decimate modifier, Ratio = 0.01








Landing on Surface


add Cylinder and Boolean-Intersect it from crater to get circular shape





go to Weight Paint mode and click in center from top view to get gradient





search for "Invert" to get red color of gradient from center on edge





add any "land" object (surface you want to follow) 
use snap tool to bring center of crater object to surface (with "Align Rotation to Target")





add to the crater object Shrinkwrap modifier and choose a Vertex Group (in this case called "Group" generated by Weight Paint mode automatically)





Works for concave and convex shapes as well ...




In this particular case (crater) probably could be enough to duplicate and rotate / scale object, that will brings illusion of crater variations without needs to make them unique, but you can sculpt a bit each of them to make more variations.